1. Field of the Invention
The present invention relates to filters, and is concerned, more particularly, with interpolative filters.
2. Description of the Prior Art
The techniques of interpolation are employed in integrated circuits for the purpose of increasing the sampling frequency of a digital signal before its conversion into an analog signal.
This technique is necessary in order to limit the out-of-band energy constituted by the image frequencies present in the frequency spectrum of the sample signal, and is employed in the majority of signal processing systems.
The interpolation of a digital signal is carried out by low-pass digital filtering associated with an increase in the sampling frequency.
In the current of the art, a simple low-pass filter forms an average of p+1 samples, which is represented in the z field by the transfer function: EQU H(z)=1+z.sup.-1 +z.sup.-2 +. . . +z.sup.-p
A well-known construction of such a filter is based on the relation: EQU 1+z.sup.-1 +z.sup.-2 +. . . +z.sup.-p =(1-z.sup.-p-1)/(l-z .sup.-1),
and utilizes a line of p+1 delays, a differentiator and an integrator.
This same construction has been adapted and generalized to interpolative filters in a structure, referred to as a cascaded integrator-comb CIC structure, composed of a cascade of differentiators and of a cascade of integrators. Between the two cascades there is interposed a change of the sampling frequency. The structure of this class of interpolative digital filters has been described in a publication by B. HOGENAUER, (IEEE, ICAASP proceedings 1980, p. 271).
A CIC filter of this type is composed of N differentiating stages connected in series, followed by an identical number N of integrating stages.
The number N of stages determines the order of the filter, and thus the attenuation of the image spectra.
The change of sampling frequency is carried out between the output of the set of differentiators and the input of the set of integrators.
The frequency change ratio is designated k. Such a known filter structure exhibits two major disadvantages:
First of all, it is necessary to initialize the integrators which are never reupdated and indefinitely maintain a shift equal to the initial value.
Then, the number of bits in the integrators increases at each stage as a function of the ratio k between the output and input sampling frequencies of the filter. This may lead to register widths which are far too large, especially if the order of the filter and the interpolation ratio are high.